Question

A new car is purchased for the price of $35,000. If the value of the car depreciates at a rate of 12% per year, when will the car be worth half of the original rate?

I put down (this was wrong): 35000 (0.12/12) = 75000
350 (0.12/12) 175 = 612.5
= about 6 years

Answer 1

V = Vo(1-r)^t = 35,000/2
35,000(1-0.12)^t = 17,500
Divide both sides by 35,000:
(0.88)^t = 0.5
Take Log of both sides:
t*Log(0.88) = Log 0.5
t = Log 0.5/Log(0.88) = 5.42 Years.